[ª] , [©] , [^] , [¨]Adding feet of perpendiculars to triangle / Drawing by tool and exploring with moving(GC World : Various Problems ,What will occur when something is added?)
Let's draw a triangle.
And let's add perpendiculars from B and C to the respective opposite sides.
Can a similar triangle be made?
Or can you make a similar triangle to ĢABC based on this figure?


If you use DGS to find the answer of this question, you can observe various cases by moving figure.
It is difficult to think the proof, but you may find an interesting result. How about this?

GC/Win


Forum of Geometric Constructor by Y.Iijima